= Thermal damping of a sinusoidal density of states
{title2=$R_T=X/\sinh X,\quad X=2\pi^2k_BT/\Delta$}
A <density of states> $g(\epsilon)=g_0[1+\alpha\cos(2\pi\epsilon/\Delta)]$ has zero-temperature oscillatory <grand potential> $g_0\alpha\Delta^2\cos(2\pi\mu/\Delta)/(4\pi^2)$. Its Fermi-window <convolution> multiplies that <oscillation> by $R_T$ when the lower band edge is far below the <chemical potential>. The <Fourier transform> of the even window removes its <sine> component and gives the title factor. At high $X$, $R_T\sim2Xe^{-X}$; at small $X$, $R_T=1-X^2/6+O(X^4)$. The corresponding thermal change relative to zero <temperature> has <amplitude> proportional to $1-R_T$, rather than $R_T$.
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